Seeking mathematical strategies in sperm function analysis: between scylla and charybdis?

During the last decades, essential progresses in reproductive biotechnology were achieved, implying development of special spermatological techniques. The major problem was to set up simple, rapid, precise and adequate evaluation methods. The key aspect to be considered in all assays of sperm fertilizing function is capacitation. As not all spermatozoa respond to fertilizing conditions in a similar manner, it seems to be logical to assess samples via their response to these specific conditions. For the spermatological practice, the sensitivity of methodology for assessment and analysis of data with respect to differences in individual response, in heterogeneity of the population, and proper temporal characterization of the response is crucial for the improvement of evaluation procedures. Currently, most used statistical analytical tools in spermatology do not always fulfil these essential sensitivity requirements. We structured our paper concerning different fields of mathematical science (distribution analysis, fractal geometry, functional approximation and differentiation) related to the modern insights in sperm function analysis. The spectrum of methods we are going to review in this paper is restricted to basic ideas to illustrate how the accuracy and sensitivity of sperm evaluation assays may be improved by applying adequate elementary tools of the mathematical analysis.